Practice Problem 41  Back  Index  Next 
Given: A cylindrical concrete column of diameter 3.5 ft. has initial height of 25.0 ft. Assume the density of concrete is 145 lb/ft^{3} and the elastic modulus in compression is 2.5 Msi. Req'd: Determine the downward displacement of the top of the column d due to its own weight. (Note: the elongation D of the column should be negative; the downward displacement d positive). 

Sol'n: Since the load is varies along the length of the column, integration is used. The best approach is to convert all lengths and units to inches and integrate the elongations of each infinitesimal length dx:
Integrating gives the change in length:
Thus, the downward displacement of the top of the column is:

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